A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations

In this paper we first introduce a new definition for the conformance of tuples existing in a fuzzy database relation. Then we give the formal definitions of fuzzy functional and multivalued dependencies on the basis of the conformance values presented here. Secondly, we list the inference rules after showing that both fuzzy functional and multivalued dependencies are consistent, that is, they reduce to those of the classic functional and multivalued dependencies when crisp attributes are involved. Finally, we show that the inference rules presented here are sound and complete for the family of functional and multivalued dependencies in fuzzy database relations